Sortable floating point numbers

Abstract

The invention comprises methods for manipulating floating point numbers on a microprocessor where the numbers are sortable. That is, the numbers obey lexicographical ordering. Hence, the numbers may be quickly compared using bit-wise comparison functions such as memcmp( ). Conversion may result in a sortable floating point number in the form of a sign, leading bits of the exponent, and sets of digit triples in the form of declets (sets of 10 bits). In a variable-length version, numbers may be compressed by storing the number of trailing zero declets in lieu of storing the zero declets themselves.

What is claimed is: 
     
       1. A method for decoding a sortable floating point number in a variable-length format into an output number on a processor comprising:
 retrieving, by the processor, the number of trailing 0 declets from a Z field; 
 unbiasing, by the processor, declets, from the second most significant declet to the last declet that contains portions of the exponent-significand field; 
 retrieving, by the processor, a sign of the number from a sign field of the sortable floating point number; and 
 retrieving, by the processor, the exponent and a significand from an exponent-significand field by applying a value-to-BCD transformation on a exponent-significand field of the sortable floating point number. 
 
     
     
       2. A method for decoding a sortable floating point number into an output number on a processor comprising:
 retrieving, by the processor, a sign of the number from a sign field of the sortable floating point number; 
 retrieving, by the processor, leading bits of an exponent from a leading exponent field; 
 retrieving, by the processor, the remaining digits of the exponent and a significand from an exponent-significand field by applying a value-to-BCD transformation on a exponent-significand field of the sortable floating point number; 
 combining, by the processor, the leading bits of the exponent and the remaining digits of the exponent to yield the exponent; 
 if the sign of the sortable floating point number is negative, shifting, by the processor, the exponent and significand; 
 assembling, by the processor, the output number from the sign, the exponent, and the significand; 
 compressing, by the processor, the output number. 
 
     
     
       3. The method of  claim 2 , wherein the number had been encoded by:
 decompressing an input number; 
 normalizing the input number; 
 if the input number is less than 0, shifting the exponent and significand fields; 
 converting the sign of the input number into a sortable representation to yield a sign field; 
 creating a leading exponent field; 
 organizing an exponent-significand field into triplets with triplet digits from the remaining exponent bits and the significand of the input number; 
 applying a bcd-to-value transformation on the triplets in the exponent-significand field to yield declets; and 
 assembling the sign, leading exponent field, and exponent-significand field into the number. 
 
     
     
       4. A method for decoding a sortable floating point number in a variable-length format into an output number on a processor comprising:
 retrieving, by the processor, the number of trailing 0 declets from a Z field; 
 unbiasing, by the processor, declets, from the second most significant declet to the last declet that contains portions of the exponent-significand field; 
 retrieving, by the processor, a sign of the number from a sign field of the sortable floating point number; 
 retrieving, by the processor, leading bits of an exponent from a leading exponent field; 
 retrieving, by the processor, the remaining digits of the exponent and a significand from an exponent-significand field by applying a value-to-BCD transformation on a exponent-significand field of the sortable floating point number; 
 combining, by the processor, the leading bits of the exponent and the remaining digits of the exponent to yield the exponent; 
 if the sign of the sortable floating point number is negative, shifting, by the processor, the exponent and significand; 
 assembling the output number from the sign, the exponent, the significand, and the number of trailing zero declets; 
 compressing, by the processor, the output number. 
 
     
     
       5. The method of  claim 4 , wherein the number had been encoded by:
 decompressing an input number; 
 normalizing the input number; 
 if the input number is less than 0, shifting the exponent and significand fields; 
 converting the sign of the input number into a sortable representation to yield a sign field; 
 creating a leading exponent field; 
 organizing an exponent-significand field into triplets with triplet digits from the remaining exponent bits and the significand of the input number; 
 applying a BCD-to-value transformation on the triplets in the exponent-significand field to yield declets; 
 biasing the declets with an offset bias, from the second most significant declet to the last declet before the trailing 0 declets; 
 storing the number of trailing 0 declets in a Z field; and 
 assembling the sign field, leading exponent field, exponent-significand field, and the Z field into the number. 
 
     
     
       6. A computer-readable non-transitory medium stored thereon executable instructions that when executed by a processor perform a method for decoding a sortable floating point number in a variable-length format into an output number on a processor, the method comprising:
 retrieving the number of trailing 0 declets from a Z field; 
 unbiasing declets, from the second most significant declet to the last declet that contains portions of the exponent-significand field; 
 retrieving a sign of the number from a sign field of the sortable floating point number; and 
 retrieving the exponent and a significand from an exponent-significand field by applying a value-to-BCD transformation on a exponent-significand field of the sortable floating point number. 
 
     
     
       7. A computer-readable non-transitory medium stored thereon executable instructions that when executed by a processor perform a method for decoding a sortable floating point number into an output number on a processor comprising:
 retrieving a sign of the number from a sign field of the sortable floating point number; 
 retrieving leading bits of an exponent from a leading exponent field; 
 retrieving the remaining digits of the exponent and a significand from an exponent-significand field by applying a value-to-BCD transformation on a exponent-significand field of the sortable floating point number; 
 combining the leading bits of the exponent and the remaining digits of the exponent to yield the exponent; 
 if the sign of the sortable floating point number is negative, shifting the exponent and significand; 
 assembling the output number from the sign, the exponent, and the significand; 
 compressing the output number. 
 
     
     
       8. A computer-readable non-transitory medium stored thereon executable instructions that when executed by a processor perform a method for decoding a sortable floating point number into an output number on a processor, the method comprising:
 retrieving the number of trailing 0 declets from a Z field; 
 unbiasing declets, from the second most significant declet to the last declet that contains portions of the exponent-significand field; 
 retrieving a sign of the number from a sign field of the sortable floating point number; 
 retrieving leading bits of an exponent from a leading exponent field; 
 retrieving the remaining digits of the exponent and a significand from an exponent-significand field by applying a value-to-BCD transformation on a exponent-significand field of the sortable floating point number; 
 combining the leading bits of the exponent and the remaining digits of the exponent to yield the exponent; 
 if the sign of the sortable floating point number is negative, shifting the exponent and significand; 
 assembling the output number from the sign, the exponent, the significand, and the number of trailing zero declets; 
 compressing the output number.